DONETSK – Fighting raged in the city of Donetsk on Sunday as government forces continued to close in on the rebel stronghold and pro-Russian insurgents backed away from an unconditional cease-fire offer that they announced just the day before.

With a string of military successes and broad support for its campaign from the West and most of its domestic base, Kiev has taken a hard line against the rebel forces and promised it will only relent when the separatists surrender. Donetsk remained a ghost town on Sunday, with few civilians daring to venture outside as explosions rang out every few minutes and burnt-out buses and buildings smoldered from the night before.

In a statement Saturday, newly elected rebel leader Aleksandr Zakharchenko appeared to call for a cease-fire without stating any preconditions. But on Sunday, rebel spokeswoman Elena Nikitina repeated the rebels’ earlier stance, telling AP that talks on the conflict could only begin if the Ukrainian army withdrew from the region — something Kiev is unlikely to do.

She also denounced the government as “incapable of negotiating.”

Ukraine’s National Security and Defense Council spokesman Andriy Lysenko said that the only way for the rebels in Donetsk to save their lives would be to “lay down their arms and give up.” He said the Ukrainian side hadn’t seen the rebels show any real willingness to cooperate.

“If white flags come up and they lay down their arms, nobody is going to shoot at them,” he said. “(But) we have not seen any practical steps yet, just a statement.”

Lysenko added that the Ukrainian military’s recent successes in encircling Donetsk had bred “panic and chaos in the ranks of the rebels,” and said the Kiev government had information about rebels “deserting their posts en masse.”

Conditions were clearly deteriorating in Donetsk, the largest rebel stronghold in eastern Ukraine. AP reporters heard 25 loud explosions in as many minutes around noon. According to city council spokesman Maxim Rovinsky, at least one person was killed and 10 injured in shelling overnight, as more than 10 residential buildings, a hospital and a shop were heavily damaged in the fighting.

Rovinsky said that he believed 100,000 people had left the city of 1 million in the past week alone — adding to the 300,000 who were already estimated to have fled. He said at least 10,000 people were without electricity, and that the local government was working hard to preserve access to gas, electricity, and phone service and “avoid a humanitarian crisis.” More than 1,300 people have died in the conflict since April, according to a U.N. estimate.

“This is a real war! It’s impossible to live in this city, I’ve been sleeping in the basement for the past week,” said Inna Drobyshevskaya, a 48-year-old lawyer in Donetsk.

“We don’t want Novorossiya (New Russia) for this price,” she added, referring to a term used by rebels to describe the parts of eastern Ukraine seeking independence from the government in Kiev.

Rebel leader Zakharchenko’s apparent call for a cease-fire Saturday was met with support from Russia, where Foreign Minister Sergey Lavrov was quoted by news agency ITAR TASS as saying a truce was “not only possible, but necessary.”

“We believe the question is urgent and there can be no delay, and the issue is under the control of the Russian president,” he said. Lavrov said that Russia was reaching out to the Red Cross and the U.N. to discuss the possibility of delivering humanitarian aid to the region.

However, the rebels’ request was met warily by government officials in Kiev and in the West. Those leaders expressed concern that the move could be aimed at increasing international pressure on Ukraine to allow in a Russian aid mission. The West says that could be used as a pretext to bring Russian soldiers into Ukraine — and says 20,000 of them are massed near the Russian border with Ukraine.

Ukrainian President Petro Poroshenko and Western leaders have repeatedly accused Russia of providing arms and expertise to the rebels, something Russia denies.

He issued a statement late Saturday saying that Ukraine was prepared to accept humanitarian assistance in eastern Ukraine. But he said the aid must come in without military assistance, pass through border checkpoints under Ukrainian control and be an international mission.

Poroshenko said he and German Chancellor Angela Merkel discussed German participation in such a mission.

On Sunday, German Foreign Minister Frank-Walter Steinmer expressed “great concern” that the humanitarian situation for civilians in Donetsk and Luhansk is getting worse. He said Germany is already working with the ICRC and U.N. agencies to ensure that existing aid is coordinated and gets delivered where it is needed.

He said it was “good that there seems to be basic agreement about the delivery of humanitarian goods between Ukraine and Russia,” but said that Russian aid “must only be delivered with the express agreement of the Ukrainian government” and under the supervision of international organizations.

In Washington, the White House said President Barack Obama and Merkel agreed that any Russian intervention in Ukraine was unacceptable and would violate international law. Obama and British Prime Minister David Cameron, meanwhile, “expressed grave concern about reports that Russian military vehicles have crossed the border into Ukraine and that Russian armed forces are exercising for a ‘humanitarian intervention,'” according to Cameron’s office.

Russian-speaking eastern Ukraine was the power base for former President Viktor Yanukovych, who fled office in February after months of anti-government protests kicked off by his decision to scuttle an association agreement with the EU in favor of closer ties with Moscow. Fighting in the east began in April, one month after Russia annexed Ukraine’s Black Sea region of Crimea.